Answer:
the duration of a day increases 4.96x10^-11 s
Explanation:
According the exercise:
R=radius of Earth=6.37x10^6 m
mE=mass of Earth=5.97x10^24 kg
m=average mass of people=55 kg
n=number of population=7x10^9
M=total mass=n*m=7x10^9*55=3.85x10^11 kg
v=speed=2.5 m/s
The moment of inertia of population is:
I=(2/3)*M*R^2=(2/3)*3.85x10^11*(6.37x10^6)=1.04x10^25 kg*m^2
The time taken per revolution is:
T=2πR/v=(2π*6.37x10^6)/2.5=1.6x10^7 rev/s
The angular speed is:
w=2π/T=2π/1.6x10^7=3.9x10^-7 rad/s
The angular momentum of population is equal to:
L1=I*w=1.04x10^25*3.9x10^-7=4.08x10^18 kg*m^2/s
The angular momentum of Earth is equal to:
L2=I*w=((2/5)*me*R^2)*(2π/24)=((2/5)*5.97x10^24*(6.37x10^6)^2)*(2π/(24*60*60))=7.1x10^33 kg*m^2/s
The change in length of the day is equal to:
T´=T*(L1/L2)=(24*60*60)*(4.08x10^18/7.1x10^33)=4.96x10^-11 s
